Approximate solution of boundary-value problems of vibrating systems with distributed parameters

1978 ◽  
Vol 14 (6) ◽  
pp. 605-609
Author(s):  
Z. E. Filer
Keyword(s):  
Approximate Solution ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Distributed Parameters ◽  
Systems With Distributed Parameters ◽  
Vibrating Systems

On the Approximate Solution of Matrix Differential-Algebraic Boundary-Value Problems by the Least-Squares Method

2021 ◽  
Vol 253 (2) ◽  
pp. 323-337
Author(s):  
S. M. Chuiko ◽  
O. V. Nesmelova ◽  
M. V. Dzyuba
Keyword(s):  
Approximate Solution ◽  
Least Squares ◽  
Boundary Value Problems ◽  
Least Squares Method ◽  
Boundary Value ◽  
Matrix Differential

On the approximate solution of autonomous boundary-value problems by the Newton method

2013 ◽  
Vol 191 (3) ◽  
pp. 449-463 ◽  
Author(s):  
S. M. Chuiko ◽  
O. E. Pirus
Keyword(s):  
Approximate Solution ◽  
Boundary Value Problems ◽  
Newton Method ◽  
Boundary Value

Improving Algorithms for Learning Radial Basic Functions Networks to Solve the Boundary Value Problems

2020 ◽  
pp. 66-106
Author(s):  
Vladimir Gorbachenko ◽  
Konstantin Savenkov
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Arbitrary Dimension ◽  
Physical Object ◽  
Projection Methods ◽  
Distributed Parameters ◽  
Digital Twins ◽  
Grid Construction ◽  
Basic Functions ◽  
Mesh Less

Digital twins are widely used in modern industry. A digital twin is a computer model that copies the behavior of a physical object. Digital twins of objects with distributed parameters are mathematically boundary value problems for partial differential equation. Traditionally, such problems are solved by finite difference and finite element methods, which require a complex grid construction procedure. The numerical solution of boundary value problems employs mesh less methods that do not require grid construction. Among mesh fewer methods, projection methods that use radial basis functions (RBFs) as basic functions are popular. Methods using RBF allow us to obtain a differentiable solution at any point in the solution domain, applicable to problems of arbitrary dimension with complex computational domains. When solving the problem, the parameters of the basic functions are selected, and the weights are calculated so that the residuals obtained after the substitution of the approximate solution at the test points in the equation are zero.

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